Simplify; express your answer in exponential form. Assume $y\neq 0, n\neq 0$. $\dfrac{{(y^{4}n^{-2})^{-3}}}{{(y^{-1}n^{4})^{-4}}}$
To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${(y^{4}n^{-2})^{-3} = (y^{4})^{-3}(n^{-2})^{-3}}$ On the left, we have ${y^{4}}$ to the exponent ${-3}$ . Now ${4 \times -3 = -12}$ , so ${(y^{4})^{-3} = y^{-12}}$ Apply the ideas above to simplify the equation. $\dfrac{{(y^{4}n^{-2})^{-3}}}{{(y^{-1}n^{4})^{-4}}} = \dfrac{{y^{-12}n^{6}}}{{y^{4}n^{-16}}}$ Break up the equation by variable and simplify. $\dfrac{{y^{-12}n^{6}}}{{y^{4}n^{-16}}} = \dfrac{{y^{-12}}}{{y^{4}}} \cdot \dfrac{{n^{6}}}{{n^{-16}}} = y^{{-12} - {4}} \cdot n^{{6} - {(-16)}} = y^{-16}n^{22}$